I haven't taken a look at the games, but one thing I can think of:
different trains are available on the first day of the game.
If set the start year later, you start with faster, more powerful and higher capacity vehicles available for you to use. Those vehicles will obviously bring larger income immediately. Added to that, if your first year was in 1937, the rate of technological advancement in the game is much slower than some years later - you're further left behind in not having faster, bigger vehicles.
To expand a bit on that point: The potential profit margins are a lot higher in 1865 than in 1837, which will allow for a much faster early expansion phase. Normally, any profit earned during the first couple of decades will quickly be reinvested in more profit-generating infrastructure. It's a pure exponential, positive-feedback, runaway loop: The more you earn, the more you'll be able to invest in order to earn even more.
The growth rate tends to flatten out when the management of existing infrastructure keeps you occupied most of the time.
I don't think inflation has anything to do with the difference, if you're comparing two games, both are at same years into the game.
Maybe not. But in any case, inflation is a powerful shot in the foot, at least for pre-1900 games.